Two American fighter pilots who intercepted Syrian combat jets over northern Syria last week said they came within 2,000 feet of the planes without the Syrians aware they were being shadowed.

The tense encounter occurred after Syrian jets dropped bombs near a U.S. adviser team with Kurdish forces in northern Syria. The Pentagon warned Syria that American forces were authorized to take action to defend its troops. Syrian aircraft haven’t dropped bombs in the area since then, and the U.S. military is no longer operating continuous combat patrols there.

“I followed him around for all three of his loops,” one of the American pilots, a 38-year-old Air Force major, told USA TODAY Wednesday in the first detailed account of the incident. “He didn’t appear to have any idea I was there.”

The two pilots asked that their names be withheld for security reasons.

“The behavior stopped,” said Brig. Gen. Charles Corcoran, commander of the 380th Air Expeditionary Wing, which conducts airstrikes in Iraq and Syria from an undisclosed location in this region. “We made our point.”

The encounter highlights the complexity of the battle in Syria against the Islamic State and raises worries that a mistake could widen the war.

“The big concern is really a miscalculation,” said Lt. Gen. Jeffrey Harrigian, commander of U.S. air operations in the Middle East. “It can happen on either side.”

The U.S.-led coalition is not at war with the Syrian government or its Russian allies, and the Pentagon reached an agreement to exchange information with the Russians to avoid a miscalculation in the air, but the two sides are not cooperating.

“We made it very clear to our folks from the highest levels: We’re not at war with the Russians or Syrians,” Corcoran said. “We’re not here to shoot down Russian or Syrian airplanes.”

Russia and the United States have agreed to keep some areas off limits to Russian and Syrian aircraft, which includes Hasakah, the area bombed last week by the Syrians.

The complexities have required pilots to navigate an ambiguous environment in the crowded skies over Syria.

“I’m thinking how do I de-escalate this scenario to the best of my ability and also keep us in a safe position while doing so,” said the second pilot involved in last week's encounter, a 30-year-old captain.

After the Syrian bombing in the off-limits area, the United States put round-the-clock combat air patrols over Hasakah, and prepared its pilots to take action should the Syrians attack American forces.

Friday's incident, as described by commanders here, began in the afternoon, when a Syrian aircraft was spotted entering the airspace around Hasakah, and the pair of F-22s, already in the area, raced toward them.

The captain said he quickly got on a common radio frequency in an effort to reach the Syrian aircraft, asking the pilot to identify himself and state his intentions. There was no response.

U.S. commanders also contacted the Russians by phone to seek information, but the Russians were unaware of the Syrian action.

At that point the only way to get information was to have the American pilots approach the Syrian planes, Su-24 Fencers, to determine if they were armed or dropping bombs.

The American pilots asked permission to get closer to the Syrian aircraft to determine if they were carrying weapons on their wings or appeared to be attacking ground targets. Normally pilots are under orders to keep their distance from Russian or Syrian planes to avoid a miscalculation.

Permission was granted. One of the F-22s watched as the other maneuvered behind the Syrian aircraft to get a closer look. After about 15 minutes, the Syrian jet left the area, apparently unaware it was being followed.

Moments later a second Syrian jet entered the airspace. The American pilots repeated the sequence. Neither of the Syrian planes appeared to be carrying weapons, the pilots said.

In the air command center in Qatar, which oversees air operations in the Middle East, Maj. Gen. Jay Silveria said he was prepared to order the pilots to down the Syrian aircraft if they threatened coalition forces. “I wouldn’t have hesitated,” he said.

“All I needed at that point to shoot them down was a report from the ground that they were being attacked,” Silveria said. “We were in a perfect position to execute that with some pretty advanced weaponry.”

But reports from the ground and the American pilots confirmed that the Syrian aircraft did not drop bombs and appeared to be transiting through the area. Syria has an air base in the region, and it is not uncommon for them to fly over the area.

The F-22 is a stealth aircraft, and pilots are trained to avoid being seen by their adversaries. Commanders are considering more overt tactics in the future to send a message to the Syrians.

“From now on if it happens, it’s get out to where they can visually see us,” Corcoran said.